The main results of this paper are the discovery of infinite families of flow equivalent pairs of B5 and W5 amallamorphs and infinite families of chromatically equivalent pairs of P and W*5 homeomorphs, where B5 is K5 with one edge deleted, P is the Prism graph and W5 is the join of K1 and a cycle on 4 vertices. Six families of B5 amallamorphs, with two families having 6 parameters, and 9 families of W5 amallamorphs, with one family having 4 parameters, are discovered. Since B5 and W5 are both planar, all these results obtained can be stated in terms of chromatically equivalent pairs of B*5 and W*5 homeomorphs. Also three conjectures are made about non-existence of flow-equivalent amallamorphs or chromatically equivalent homeomorphs of certain graphs (Refer to PDF file for exact formulas).
Department, Program, or Center
School of Mathematical Sciences (COS)
Shahmohamad, Hossein, "On the equivalences of the wheel W5, the prism P and the bipyramid B5" (2003). Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 46 (), 161-170. Accessed from
RIT – Main Campus